基于弹性半空间Green函数的明置条形基础阻抗解答
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摘要
基于弹性半空间理论,在Lamb解的基础上推导了非轴对称的简谐线激振荷载及条形均布激振荷载作用下的地基Green函数。然后将明置条形基础与地基的接触面分割成若干个条形单元,根据刚体位移所决定的各单元位移,运用上述Green函数求解各单元的接触力,将所求得的力叠加即为地基阻抗函数。通过分段积分法及Cauchy主值积分对涉及的多值广义积分进行数值处理,计算了明置条形基础的垂直阻抗,观察了其收敛性,亦计算了其水平和回转动柔度,并与半解析半数值的薄层法的结果进行了比较,表现出很好的一致性。最后通过算例讨论了土体泊松比对明置条形基础阻抗的影响。
Non-axisymmetric Green functions of the elastic half-space under harmonic line load and uniform load with infinite length were derived based on the Lamb's solution.The interface between the foundation and the supporting medium was divided into a number of strip elements.A piecewise integration method was used to calculate the multi-value improper integral.The impedance function was solved by adding the contact forces on each strip,based on the fact that the displacement of the rigid foundation determines that of each elements.The vertical impedance of a surface-supported strip foundation was calculated and its convergence was observed.The horizon and rotational impedances were compared with those obtained from the thin layer method(TLM).Agreements between the present results and the TLM results were observed.Finally,the effect of Poisson's ratio on impedance functions was discussed in detail.
Non-axisymmetric Green functions of the elastic half-space under harmonic line load and uniform load with infinite length were derived based on the Lamb's solution.The interface between the foundation and the supporting medium was divided into a number of strip elements.A piecewise integration method was used to calculate the multi-value improper integral.The impedance function was solved by adding the contact forces on each strip,based on the fact that the displacement of the rigid foundation determines that of each elements.The vertical impedance of a surface-supported strip foundation was calculated and its convergence was observed.The horizon and rotational impedances were compared with those obtained from the thin layer method(TLM).Agreements between the present results and the TLM results were observed.Finally,the effect of Poisson's ratio on impedance functions was discussed in detail.
引文
[1]STATIONARE R E.Axialsymmetrische durch eine sehuttelnde masse erregte sehwingungen-eines homogenen elastisehen hal-braumes[J].Ingenieur-Arch,1936,7(6):381-396.
[2]WOLF J P.Dynamic Soil-Structure Interaction[M].Englewood Cliffs,NJ:Prentice-Hall,1985.
[3]日本建筑学会.建物と地盤の動的相互作用を考慮した応答解析と耐震設計[M].東京:日本建筑学会,2006.
[4]蒋通,田治见宏.地基结构动力相互作用分析方法[M].上海:同济大学出版社,2009.
[5]SUNG T Y.Vibration in semi-infinite solids due to periodic surface loadings[J].Symposium of Dynamic Testing of Soils,1953,156(1):35-64.
[6]ARNOLD R N,BYCROFT G N,WARBURTON G B.Forced vibrations of a body on an infinite elastic solid[J].Journal of Applied Mechanics,1955,77(3):391-400.
[7]BYCROFT G N.Forced vibrations of a rigid circular plate on a semi-infinite elastic space and on an elastic stratum[J].Philosophical Transactions of the Royal Society,Series A,1956,248(948):327-368.
[8]李刚,王贻荪,尚守平.弹性半空间上矩形基础稳态振动积分变换解[J].湖南大学学报:自然科学版,2000,27(4):88-93.
[9]AWOJOBI A O,Grootenhuis P.Vibration of rigid bodies on semi-infinite elastic media[J].Proceedings of the Royal Society,Series A.1965,287(1408):27-63.
[10]LUCO J E,WESTMANN R A.Dynamic response of a rigid footing bonded to an elastic half-space[J].J Eng Mech Div ASME,1972,39(2):527-534..
[11]VELETSOS A S,WEI Y T.Lateral and rocking vibration of footings[J].Journal of Soil Mechanics and Foundations Division,ASCE,1971,97(9):1227-1248.
[12]VELETSOS A S,Nair V V D.Torsional vibration of viscoelastic foundations[J].Journal of the Geotechnical Engineering Division,ASCE,1974,100(3):225-246.
[13]LAMB H.On the propagation over the surface of an elastic solid[J].Philosophical Transaction of the Royal Society,London,Series A,1904,203(1):1-42.
[14]DAVIS P J,PHILIP R.Methods of Numerical Integration:Second Edition[M].New York:Dover Publications,2007.
[15]蒋通,宋晓星.用薄层法分析层状地基中条形基础的阻抗函数[J].力学季刊,2009,30(1):62-70.
[16]林皋,栾茂田,陈怀海.土-结构相互作用对高层建筑非线性地震反应的影响[J].土木工程学报,1993,26(4):1-13.
[2]WOLF J P.Dynamic Soil-Structure Interaction[M].Englewood Cliffs,NJ:Prentice-Hall,1985.
[3]日本建筑学会.建物と地盤の動的相互作用を考慮した応答解析と耐震設計[M].東京:日本建筑学会,2006.
[4]蒋通,田治见宏.地基结构动力相互作用分析方法[M].上海:同济大学出版社,2009.
[5]SUNG T Y.Vibration in semi-infinite solids due to periodic surface loadings[J].Symposium of Dynamic Testing of Soils,1953,156(1):35-64.
[6]ARNOLD R N,BYCROFT G N,WARBURTON G B.Forced vibrations of a body on an infinite elastic solid[J].Journal of Applied Mechanics,1955,77(3):391-400.
[7]BYCROFT G N.Forced vibrations of a rigid circular plate on a semi-infinite elastic space and on an elastic stratum[J].Philosophical Transactions of the Royal Society,Series A,1956,248(948):327-368.
[8]李刚,王贻荪,尚守平.弹性半空间上矩形基础稳态振动积分变换解[J].湖南大学学报:自然科学版,2000,27(4):88-93.
[9]AWOJOBI A O,Grootenhuis P.Vibration of rigid bodies on semi-infinite elastic media[J].Proceedings of the Royal Society,Series A.1965,287(1408):27-63.
[10]LUCO J E,WESTMANN R A.Dynamic response of a rigid footing bonded to an elastic half-space[J].J Eng Mech Div ASME,1972,39(2):527-534..
[11]VELETSOS A S,WEI Y T.Lateral and rocking vibration of footings[J].Journal of Soil Mechanics and Foundations Division,ASCE,1971,97(9):1227-1248.
[12]VELETSOS A S,Nair V V D.Torsional vibration of viscoelastic foundations[J].Journal of the Geotechnical Engineering Division,ASCE,1974,100(3):225-246.
[13]LAMB H.On the propagation over the surface of an elastic solid[J].Philosophical Transaction of the Royal Society,London,Series A,1904,203(1):1-42.
[14]DAVIS P J,PHILIP R.Methods of Numerical Integration:Second Edition[M].New York:Dover Publications,2007.
[15]蒋通,宋晓星.用薄层法分析层状地基中条形基础的阻抗函数[J].力学季刊,2009,30(1):62-70.
[16]林皋,栾茂田,陈怀海.土-结构相互作用对高层建筑非线性地震反应的影响[J].土木工程学报,1993,26(4):1-13.
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